Abstract

We investigate the properties of the resonant modes that occur in the transparency bands of two-dimensional finite-size Penrose-type photonic quasicrystals made of dielectric cylindrical rods. These modes stem from the natural local arrangements of the quasicrystal structure rather than, as originally thought, from fabrication-related imperfections. Examples of local density of states and field maps are shown for different wavelengths. Calculations of local density of states show that these modes mainly originate from the interactions between a limited numbers of rods.

©2006 Optical Society of America

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  1. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart, and Winston, New York, 1976).
  2. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059 (1987).
    [Crossref] [PubMed]
  3. D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, “Metallic phase with long-range orientational order and no translation symmetry,” Phys. Rev. Lett. 53, 1951 (1984).
    [Crossref]
  4. W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72, 633 (1994).
    [Crossref] [PubMed]
  5. T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, “Photonic dispersion relation in a one-dimensional quasicrystal”, Phys. Rev. B. 50, R4220 (1994).
    [Crossref]
  6. F. Zolla, D. Felbacq, and B. Guizal, “A remarkable diffractive property of photonic quasi-crystals,” Opt. Comm. 148, 6 (1998).
    [Crossref]
  7. L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 55501 (2003).
    [Crossref]
  8. Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett. 80, 956 (1998).
    [Crossref]
  9. M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. M. De La Rue, and P. Millar, “Two-dimensional Penrose-tiled photonic quasicrystals: Diffraction of light and fractal density of modes,” J. Mod. Opt. 47, 1771 (2000).
  10. M. E. Zoorob, M. D. B. Charleton, G. J. Parker, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404, 740743 (2000).
  11. X. Zhang, Z.-Q. Zhang, and C. T. Chan, “Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals,” Phys. Rev. B 63, R081105 (2001).
    [Crossref]
  12. M. Bayndir, E. Cubukcu, I. Bulu, and E. Ozbay, “Photonic band-gap effect, localization, and waveguiding in the two-dimensional Penroselattice,” Phys. Rev. B. 63R161104 (2001).
    [Crossref]
  13. A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Bandgap formation and multiple scattering in photonic quasicrystals with Penrose lattice,” Phys. Rev. Lett. 94, 183903 (2005).
    [Crossref] [PubMed]
  14. M. Notomi, H. Suzuki, T. Tamamura, and K. Edagawa, “Lasing action due to the two-dimensional quasiperiodicity of photonic quasicrystals with a Penrose lattice,” Phys. Rev. Lett. 92, 123906 (2004).
    [Crossref] [PubMed]
  15. Y. Wang, X. Hu, X. Xu, B. Cheng, and D. Zhang, “Localized modes in defect-free dodecagonal quasiperiodic photonic crystals,” Phys. Rev. B 68, 165106 (2003).
    [Crossref]
  16. M. Senechal, Quasicrystals and geometry (Cambridge University Press, Cambridge, 1995)
  17. D. Felbacq, G. Tayeb, and D. Maystre, “Scattering by a random set of parallel cylinders,” J. Opt. Soc. Am. A 11, 2526 (1994).
    [Crossref]
  18. N. A. Nicorovici, R. C. McPhedran, and L.C. Botten, “Photonic band gaps for arrays of perfectly conducting cylinders,” Phys. Rev. E 52, 1135 (1995).
    [Crossref]
  19. J. Korringa, “On the calculation of the energy of a Bloch wave in a metal,” Physica 13, 392 (1947); W. Kohn and N. Rostoker, “Solution of the Schrödinger equation in periodic lattices with an application to metallic lithium,” Phys. Rev. 94, 1111 (1954).
    [Crossref]
  20. A. A. Asatryan, S. Fabre, K. Busch, R. McPhedran, L. Botten, M. de Sterke, and N. A. Nicorovici, “Two-dimensional local density of states in two-dimensional photonic crystals,” Opt. Express 8, 191 (2001).
    [Crossref] [PubMed]
  21. A. A. Asatryan, K. Busch, R. C. McPhedran, L. C. Botten, C. Martijn de Sterke, and N. A. Nicorovici, “Two-dimensional Green’s function and local density of states in photonic crystals consisting of a finite number of cylinders of infinite length,” Phys. Rev. E 63, 46612 (2001).
    [Crossref]

2005 (1)

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Bandgap formation and multiple scattering in photonic quasicrystals with Penrose lattice,” Phys. Rev. Lett. 94, 183903 (2005).
[Crossref] [PubMed]

2004 (1)

M. Notomi, H. Suzuki, T. Tamamura, and K. Edagawa, “Lasing action due to the two-dimensional quasiperiodicity of photonic quasicrystals with a Penrose lattice,” Phys. Rev. Lett. 92, 123906 (2004).
[Crossref] [PubMed]

2003 (2)

Y. Wang, X. Hu, X. Xu, B. Cheng, and D. Zhang, “Localized modes in defect-free dodecagonal quasiperiodic photonic crystals,” Phys. Rev. B 68, 165106 (2003).
[Crossref]

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 55501 (2003).
[Crossref]

2001 (4)

X. Zhang, Z.-Q. Zhang, and C. T. Chan, “Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals,” Phys. Rev. B 63, R081105 (2001).
[Crossref]

M. Bayndir, E. Cubukcu, I. Bulu, and E. Ozbay, “Photonic band-gap effect, localization, and waveguiding in the two-dimensional Penroselattice,” Phys. Rev. B. 63R161104 (2001).
[Crossref]

A. A. Asatryan, S. Fabre, K. Busch, R. McPhedran, L. Botten, M. de Sterke, and N. A. Nicorovici, “Two-dimensional local density of states in two-dimensional photonic crystals,” Opt. Express 8, 191 (2001).
[Crossref] [PubMed]

A. A. Asatryan, K. Busch, R. C. McPhedran, L. C. Botten, C. Martijn de Sterke, and N. A. Nicorovici, “Two-dimensional Green’s function and local density of states in photonic crystals consisting of a finite number of cylinders of infinite length,” Phys. Rev. E 63, 46612 (2001).
[Crossref]

2000 (2)

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. M. De La Rue, and P. Millar, “Two-dimensional Penrose-tiled photonic quasicrystals: Diffraction of light and fractal density of modes,” J. Mod. Opt. 47, 1771 (2000).

M. E. Zoorob, M. D. B. Charleton, G. J. Parker, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404, 740743 (2000).

1998 (2)

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett. 80, 956 (1998).
[Crossref]

F. Zolla, D. Felbacq, and B. Guizal, “A remarkable diffractive property of photonic quasi-crystals,” Opt. Comm. 148, 6 (1998).
[Crossref]

1995 (1)

N. A. Nicorovici, R. C. McPhedran, and L.C. Botten, “Photonic band gaps for arrays of perfectly conducting cylinders,” Phys. Rev. E 52, 1135 (1995).
[Crossref]

1994 (3)

D. Felbacq, G. Tayeb, and D. Maystre, “Scattering by a random set of parallel cylinders,” J. Opt. Soc. Am. A 11, 2526 (1994).
[Crossref]

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72, 633 (1994).
[Crossref] [PubMed]

T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, “Photonic dispersion relation in a one-dimensional quasicrystal”, Phys. Rev. B. 50, R4220 (1994).
[Crossref]

1987 (1)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059 (1987).
[Crossref] [PubMed]

1984 (1)

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, “Metallic phase with long-range orientational order and no translation symmetry,” Phys. Rev. Lett. 53, 1951 (1984).
[Crossref]

1947 (1)

J. Korringa, “On the calculation of the energy of a Bloch wave in a metal,” Physica 13, 392 (1947); W. Kohn and N. Rostoker, “Solution of the Schrödinger equation in periodic lattices with an application to metallic lithium,” Phys. Rev. 94, 1111 (1954).
[Crossref]

J. Korringa, “On the calculation of the energy of a Bloch wave in a metal,” Physica 13, 392 (1947); W. Kohn and N. Rostoker, “Solution of the Schrödinger equation in periodic lattices with an application to metallic lithium,” Phys. Rev. 94, 1111 (1954).
[Crossref]

Abram, R. A.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. M. De La Rue, and P. Millar, “Two-dimensional Penrose-tiled photonic quasicrystals: Diffraction of light and fractal density of modes,” J. Mod. Opt. 47, 1771 (2000).

Asatryan, A. A.

A. A. Asatryan, S. Fabre, K. Busch, R. McPhedran, L. Botten, M. de Sterke, and N. A. Nicorovici, “Two-dimensional local density of states in two-dimensional photonic crystals,” Opt. Express 8, 191 (2001).
[Crossref] [PubMed]

A. A. Asatryan, K. Busch, R. C. McPhedran, L. C. Botten, C. Martijn de Sterke, and N. A. Nicorovici, “Two-dimensional Green’s function and local density of states in photonic crystals consisting of a finite number of cylinders of infinite length,” Phys. Rev. E 63, 46612 (2001).
[Crossref]

Ashcroft, N. W.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart, and Winston, New York, 1976).

Baumberg, J. J.

M. E. Zoorob, M. D. B. Charleton, G. J. Parker, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404, 740743 (2000).

Bayndir, M.

M. Bayndir, E. Cubukcu, I. Bulu, and E. Ozbay, “Photonic band-gap effect, localization, and waveguiding in the two-dimensional Penroselattice,” Phys. Rev. B. 63R161104 (2001).
[Crossref]

Blech, I.

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, “Metallic phase with long-range orientational order and no translation symmetry,” Phys. Rev. Lett. 53, 1951 (1984).
[Crossref]

Botten, L.

Botten, L. C.

A. A. Asatryan, K. Busch, R. C. McPhedran, L. C. Botten, C. Martijn de Sterke, and N. A. Nicorovici, “Two-dimensional Green’s function and local density of states in photonic crystals consisting of a finite number of cylinders of infinite length,” Phys. Rev. E 63, 46612 (2001).
[Crossref]

Botten, L.C.

N. A. Nicorovici, R. C. McPhedran, and L.C. Botten, “Photonic band gaps for arrays of perfectly conducting cylinders,” Phys. Rev. E 52, 1135 (1995).
[Crossref]

Brand, S.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. M. De La Rue, and P. Millar, “Two-dimensional Penrose-tiled photonic quasicrystals: Diffraction of light and fractal density of modes,” J. Mod. Opt. 47, 1771 (2000).

Bulu, I.

M. Bayndir, E. Cubukcu, I. Bulu, and E. Ozbay, “Photonic band-gap effect, localization, and waveguiding in the two-dimensional Penroselattice,” Phys. Rev. B. 63R161104 (2001).
[Crossref]

Busch, K.

A. A. Asatryan, K. Busch, R. C. McPhedran, L. C. Botten, C. Martijn de Sterke, and N. A. Nicorovici, “Two-dimensional Green’s function and local density of states in photonic crystals consisting of a finite number of cylinders of infinite length,” Phys. Rev. E 63, 46612 (2001).
[Crossref]

A. A. Asatryan, S. Fabre, K. Busch, R. McPhedran, L. Botten, M. de Sterke, and N. A. Nicorovici, “Two-dimensional local density of states in two-dimensional photonic crystals,” Opt. Express 8, 191 (2001).
[Crossref] [PubMed]

Cahn, J. W.

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, “Metallic phase with long-range orientational order and no translation symmetry,” Phys. Rev. Lett. 53, 1951 (1984).
[Crossref]

Capolino, F.

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Bandgap formation and multiple scattering in photonic quasicrystals with Penrose lattice,” Phys. Rev. Lett. 94, 183903 (2005).
[Crossref] [PubMed]

Chan, C. T.

X. Zhang, Z.-Q. Zhang, and C. T. Chan, “Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals,” Phys. Rev. B 63, R081105 (2001).
[Crossref]

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett. 80, 956 (1998).
[Crossref]

Chan, Y. S.

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett. 80, 956 (1998).
[Crossref]

Charleton, M. D. B.

M. E. Zoorob, M. D. B. Charleton, G. J. Parker, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404, 740743 (2000).

Cheng, B.

Y. Wang, X. Hu, X. Xu, B. Cheng, and D. Zhang, “Localized modes in defect-free dodecagonal quasiperiodic photonic crystals,” Phys. Rev. B 68, 165106 (2003).
[Crossref]

Colocci, M.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 55501 (2003).
[Crossref]

Cubukcu, E.

M. Bayndir, E. Cubukcu, I. Bulu, and E. Ozbay, “Photonic band-gap effect, localization, and waveguiding in the two-dimensional Penroselattice,” Phys. Rev. B. 63R161104 (2001).
[Crossref]

Dal Negro, L.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 55501 (2003).
[Crossref]

De La Rue, R. M.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. M. De La Rue, and P. Millar, “Two-dimensional Penrose-tiled photonic quasicrystals: Diffraction of light and fractal density of modes,” J. Mod. Opt. 47, 1771 (2000).

de Sterke, M.

Della Villa, A.

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Bandgap formation and multiple scattering in photonic quasicrystals with Penrose lattice,” Phys. Rev. Lett. 94, 183903 (2005).
[Crossref] [PubMed]

Edagawa, K.

M. Notomi, H. Suzuki, T. Tamamura, and K. Edagawa, “Lasing action due to the two-dimensional quasiperiodicity of photonic quasicrystals with a Penrose lattice,” Phys. Rev. Lett. 92, 123906 (2004).
[Crossref] [PubMed]

Enoch, S.

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Bandgap formation and multiple scattering in photonic quasicrystals with Penrose lattice,” Phys. Rev. Lett. 94, 183903 (2005).
[Crossref] [PubMed]

Fabre, S.

Felbacq, D.

F. Zolla, D. Felbacq, and B. Guizal, “A remarkable diffractive property of photonic quasi-crystals,” Opt. Comm. 148, 6 (1998).
[Crossref]

D. Felbacq, G. Tayeb, and D. Maystre, “Scattering by a random set of parallel cylinders,” J. Opt. Soc. Am. A 11, 2526 (1994).
[Crossref]

Gaburro, Z.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 55501 (2003).
[Crossref]

Galdi, V.

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Bandgap formation and multiple scattering in photonic quasicrystals with Penrose lattice,” Phys. Rev. Lett. 94, 183903 (2005).
[Crossref] [PubMed]

Gellermann, W.

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72, 633 (1994).
[Crossref] [PubMed]

Gratias, D.

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, “Metallic phase with long-range orientational order and no translation symmetry,” Phys. Rev. Lett. 53, 1951 (1984).
[Crossref]

Guizal, B.

F. Zolla, D. Felbacq, and B. Guizal, “A remarkable diffractive property of photonic quasi-crystals,” Opt. Comm. 148, 6 (1998).
[Crossref]

Hattori, T.

T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, “Photonic dispersion relation in a one-dimensional quasicrystal”, Phys. Rev. B. 50, R4220 (1994).
[Crossref]

Hu, X.

Y. Wang, X. Hu, X. Xu, B. Cheng, and D. Zhang, “Localized modes in defect-free dodecagonal quasiperiodic photonic crystals,” Phys. Rev. B 68, 165106 (2003).
[Crossref]

Johnson, P.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 55501 (2003).
[Crossref]

Kaliteevski, M. A.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. M. De La Rue, and P. Millar, “Two-dimensional Penrose-tiled photonic quasicrystals: Diffraction of light and fractal density of modes,” J. Mod. Opt. 47, 1771 (2000).

Kawato, S.

T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, “Photonic dispersion relation in a one-dimensional quasicrystal”, Phys. Rev. B. 50, R4220 (1994).
[Crossref]

Kohmoto, M.

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72, 633 (1994).
[Crossref] [PubMed]

Kohn, W.

J. Korringa, “On the calculation of the energy of a Bloch wave in a metal,” Physica 13, 392 (1947); W. Kohn and N. Rostoker, “Solution of the Schrödinger equation in periodic lattices with an application to metallic lithium,” Phys. Rev. 94, 1111 (1954).
[Crossref]

Korringa, J.

J. Korringa, “On the calculation of the energy of a Bloch wave in a metal,” Physica 13, 392 (1947); W. Kohn and N. Rostoker, “Solution of the Schrödinger equation in periodic lattices with an application to metallic lithium,” Phys. Rev. 94, 1111 (1954).
[Crossref]

Krauss, T. F.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. M. De La Rue, and P. Millar, “Two-dimensional Penrose-tiled photonic quasicrystals: Diffraction of light and fractal density of modes,” J. Mod. Opt. 47, 1771 (2000).

Lagendijk, A.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 55501 (2003).
[Crossref]

Liu, Z. Y.

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett. 80, 956 (1998).
[Crossref]

Martijn de Sterke, C.

A. A. Asatryan, K. Busch, R. C. McPhedran, L. C. Botten, C. Martijn de Sterke, and N. A. Nicorovici, “Two-dimensional Green’s function and local density of states in photonic crystals consisting of a finite number of cylinders of infinite length,” Phys. Rev. E 63, 46612 (2001).
[Crossref]

Maystre, D.

McPhedran, R.

McPhedran, R. C.

A. A. Asatryan, K. Busch, R. C. McPhedran, L. C. Botten, C. Martijn de Sterke, and N. A. Nicorovici, “Two-dimensional Green’s function and local density of states in photonic crystals consisting of a finite number of cylinders of infinite length,” Phys. Rev. E 63, 46612 (2001).
[Crossref]

N. A. Nicorovici, R. C. McPhedran, and L.C. Botten, “Photonic band gaps for arrays of perfectly conducting cylinders,” Phys. Rev. E 52, 1135 (1995).
[Crossref]

Mermin, N. D.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart, and Winston, New York, 1976).

Millar, P.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. M. De La Rue, and P. Millar, “Two-dimensional Penrose-tiled photonic quasicrystals: Diffraction of light and fractal density of modes,” J. Mod. Opt. 47, 1771 (2000).

Nakatsuka, H.

T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, “Photonic dispersion relation in a one-dimensional quasicrystal”, Phys. Rev. B. 50, R4220 (1994).
[Crossref]

Netti, M. C.

M. E. Zoorob, M. D. B. Charleton, G. J. Parker, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404, 740743 (2000).

Nicorovici, N. A.

A. A. Asatryan, K. Busch, R. C. McPhedran, L. C. Botten, C. Martijn de Sterke, and N. A. Nicorovici, “Two-dimensional Green’s function and local density of states in photonic crystals consisting of a finite number of cylinders of infinite length,” Phys. Rev. E 63, 46612 (2001).
[Crossref]

A. A. Asatryan, S. Fabre, K. Busch, R. McPhedran, L. Botten, M. de Sterke, and N. A. Nicorovici, “Two-dimensional local density of states in two-dimensional photonic crystals,” Opt. Express 8, 191 (2001).
[Crossref] [PubMed]

N. A. Nicorovici, R. C. McPhedran, and L.C. Botten, “Photonic band gaps for arrays of perfectly conducting cylinders,” Phys. Rev. E 52, 1135 (1995).
[Crossref]

Notomi, M.

M. Notomi, H. Suzuki, T. Tamamura, and K. Edagawa, “Lasing action due to the two-dimensional quasiperiodicity of photonic quasicrystals with a Penrose lattice,” Phys. Rev. Lett. 92, 123906 (2004).
[Crossref] [PubMed]

Oton, C. J.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 55501 (2003).
[Crossref]

Ozbay, E.

M. Bayndir, E. Cubukcu, I. Bulu, and E. Ozbay, “Photonic band-gap effect, localization, and waveguiding in the two-dimensional Penroselattice,” Phys. Rev. B. 63R161104 (2001).
[Crossref]

Parker, G. J.

M. E. Zoorob, M. D. B. Charleton, G. J. Parker, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404, 740743 (2000).

Pavesi, L.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 55501 (2003).
[Crossref]

Pierro, V.

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Bandgap formation and multiple scattering in photonic quasicrystals with Penrose lattice,” Phys. Rev. Lett. 94, 183903 (2005).
[Crossref] [PubMed]

Righini, R.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 55501 (2003).
[Crossref]

Rostoker, N.

J. Korringa, “On the calculation of the energy of a Bloch wave in a metal,” Physica 13, 392 (1947); W. Kohn and N. Rostoker, “Solution of the Schrödinger equation in periodic lattices with an application to metallic lithium,” Phys. Rev. 94, 1111 (1954).
[Crossref]

Senechal, M.

M. Senechal, Quasicrystals and geometry (Cambridge University Press, Cambridge, 1995)

Shechtman, D.

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, “Metallic phase with long-range orientational order and no translation symmetry,” Phys. Rev. Lett. 53, 1951 (1984).
[Crossref]

Sutherland, B.

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72, 633 (1994).
[Crossref] [PubMed]

Suzuki, H.

M. Notomi, H. Suzuki, T. Tamamura, and K. Edagawa, “Lasing action due to the two-dimensional quasiperiodicity of photonic quasicrystals with a Penrose lattice,” Phys. Rev. Lett. 92, 123906 (2004).
[Crossref] [PubMed]

Tamamura, T.

M. Notomi, H. Suzuki, T. Tamamura, and K. Edagawa, “Lasing action due to the two-dimensional quasiperiodicity of photonic quasicrystals with a Penrose lattice,” Phys. Rev. Lett. 92, 123906 (2004).
[Crossref] [PubMed]

Tayeb, G.

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Bandgap formation and multiple scattering in photonic quasicrystals with Penrose lattice,” Phys. Rev. Lett. 94, 183903 (2005).
[Crossref] [PubMed]

D. Felbacq, G. Tayeb, and D. Maystre, “Scattering by a random set of parallel cylinders,” J. Opt. Soc. Am. A 11, 2526 (1994).
[Crossref]

Taylor, P. C.

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72, 633 (1994).
[Crossref] [PubMed]

Tsurumachi, N.

T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, “Photonic dispersion relation in a one-dimensional quasicrystal”, Phys. Rev. B. 50, R4220 (1994).
[Crossref]

Wang, Y.

Y. Wang, X. Hu, X. Xu, B. Cheng, and D. Zhang, “Localized modes in defect-free dodecagonal quasiperiodic photonic crystals,” Phys. Rev. B 68, 165106 (2003).
[Crossref]

Wiersma, D. S.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 55501 (2003).
[Crossref]

Xu, X.

Y. Wang, X. Hu, X. Xu, B. Cheng, and D. Zhang, “Localized modes in defect-free dodecagonal quasiperiodic photonic crystals,” Phys. Rev. B 68, 165106 (2003).
[Crossref]

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059 (1987).
[Crossref] [PubMed]

Zhang, D.

Y. Wang, X. Hu, X. Xu, B. Cheng, and D. Zhang, “Localized modes in defect-free dodecagonal quasiperiodic photonic crystals,” Phys. Rev. B 68, 165106 (2003).
[Crossref]

Zhang, X.

X. Zhang, Z.-Q. Zhang, and C. T. Chan, “Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals,” Phys. Rev. B 63, R081105 (2001).
[Crossref]

Zhang, Z.-Q.

X. Zhang, Z.-Q. Zhang, and C. T. Chan, “Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals,” Phys. Rev. B 63, R081105 (2001).
[Crossref]

Zolla, F.

F. Zolla, D. Felbacq, and B. Guizal, “A remarkable diffractive property of photonic quasi-crystals,” Opt. Comm. 148, 6 (1998).
[Crossref]

Zoorob, M. E.

M. E. Zoorob, M. D. B. Charleton, G. J. Parker, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404, 740743 (2000).

J. Mod. Opt. (1)

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. M. De La Rue, and P. Millar, “Two-dimensional Penrose-tiled photonic quasicrystals: Diffraction of light and fractal density of modes,” J. Mod. Opt. 47, 1771 (2000).

J. Opt. Soc. Am. A (1)

Nature (1)

M. E. Zoorob, M. D. B. Charleton, G. J. Parker, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404, 740743 (2000).

Opt. Comm. (1)

F. Zolla, D. Felbacq, and B. Guizal, “A remarkable diffractive property of photonic quasi-crystals,” Opt. Comm. 148, 6 (1998).
[Crossref]

Opt. Express (1)

Phys. Rev. B (2)

Y. Wang, X. Hu, X. Xu, B. Cheng, and D. Zhang, “Localized modes in defect-free dodecagonal quasiperiodic photonic crystals,” Phys. Rev. B 68, 165106 (2003).
[Crossref]

X. Zhang, Z.-Q. Zhang, and C. T. Chan, “Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals,” Phys. Rev. B 63, R081105 (2001).
[Crossref]

Phys. Rev. B. (2)

M. Bayndir, E. Cubukcu, I. Bulu, and E. Ozbay, “Photonic band-gap effect, localization, and waveguiding in the two-dimensional Penroselattice,” Phys. Rev. B. 63R161104 (2001).
[Crossref]

T. Hattori, N. Tsurumachi, S. Kawato, and H. Nakatsuka, “Photonic dispersion relation in a one-dimensional quasicrystal”, Phys. Rev. B. 50, R4220 (1994).
[Crossref]

Phys. Rev. E (2)

A. A. Asatryan, K. Busch, R. C. McPhedran, L. C. Botten, C. Martijn de Sterke, and N. A. Nicorovici, “Two-dimensional Green’s function and local density of states in photonic crystals consisting of a finite number of cylinders of infinite length,” Phys. Rev. E 63, 46612 (2001).
[Crossref]

N. A. Nicorovici, R. C. McPhedran, and L.C. Botten, “Photonic band gaps for arrays of perfectly conducting cylinders,” Phys. Rev. E 52, 1135 (1995).
[Crossref]

Phys. Rev. Lett. (7)

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90, 55501 (2003).
[Crossref]

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett. 80, 956 (1998).
[Crossref]

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059 (1987).
[Crossref] [PubMed]

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, “Metallic phase with long-range orientational order and no translation symmetry,” Phys. Rev. Lett. 53, 1951 (1984).
[Crossref]

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72, 633 (1994).
[Crossref] [PubMed]

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Bandgap formation and multiple scattering in photonic quasicrystals with Penrose lattice,” Phys. Rev. Lett. 94, 183903 (2005).
[Crossref] [PubMed]

M. Notomi, H. Suzuki, T. Tamamura, and K. Edagawa, “Lasing action due to the two-dimensional quasiperiodicity of photonic quasicrystals with a Penrose lattice,” Phys. Rev. Lett. 92, 123906 (2004).
[Crossref] [PubMed]

Physica (1)

J. Korringa, “On the calculation of the energy of a Bloch wave in a metal,” Physica 13, 392 (1947); W. Kohn and N. Rostoker, “Solution of the Schrödinger equation in periodic lattices with an application to metallic lithium,” Phys. Rev. 94, 1111 (1954).
[Crossref]

Other (2)

M. Senechal, Quasicrystals and geometry (Cambridge University Press, Cambridge, 1995)

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart, and Winston, New York, 1976).

Supplementary Material (1)

» Media 1: AVI (2028 KB)     

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Figures (6)

Fig. 1.
Fig. 1. Left: A Penrose photonic quasicrystal made of 530 dielectric rods placed at the vertices of the rhombus tiles. Right: LDOS computed at x=0, y=0. Distances are normalized with respect to a in all figs.

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Fig. 2.
Fig. 2. Left: LDOS map in linear false-color scale (red=high; blue=low) pertaining to the upper region of the photonic quasicrystal in Fig. 1, at a normalized frequency a/λ=0.415. Right: Zoom of a region (dashed square) where a fivefold symmetry of the field distribution is clearly visible. Distances are normalized with respect to a in all figs.

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Fig. 3.
Fig. 3. As in Fig. 2, but for a normalized frequency a/λ=0.726.

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Fig. 4.
Fig. 4. Electric line source excitation at x/a=1.05 and y/a=4.6, with normalized frequency a/λ=0.726. Modulus (left) and phase (right) of the electric field.

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Fig. 5.
Fig. 5. LDOS maps for photonic quasicrystals of different sizes (same color scale). From left to right: 488, 384, and 47 rods, respectively.

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Fig. 6.
Fig. 6. LDOS map for a photonic quasicrystal of 47 rods, at a normalized frequency of 0.729. See also the movie that shows the variations for normalized frequencies varying from 0.712 to 0.739. Color scales are identical to that in Fig. 5 [Media 1]

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Equations (2)

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ρ ( r 0 , ω ) = ℑ m ( G ( r = r 0 , ω ) ) .
Δ G ( r , ω ) + ε ( r ) ( ω c ) 2 G ( r , ω ) = 4 δ ( r − r 0 ) ,

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